Characterization of Finsler spaces of scalar curvature

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. E-mail: amrsoleiman@yahoo.com

2 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt. E-mail: nlyoussef2003@yahoo.fr

Abstract

In Finsler Geometry, all special spaces are investigated locally (using local coordinates) by many authors. On the other hand, the global (or intrinsic, free from local coordinates) investigation of such spaces is very rare in the literature. The aim of the present paper is to provide an intrinsic investigation of two special Finsler spaces whose defining properties are related to Berwald connection, namely, Finsler space of scalar curvature and of constant curvature. Some characterizations of a Finsler space of scalar curvature are proved. Necessary and sufficient conditions under which a Finsler space of scalar curvature reduces to a Finsler space of constant curvature are investigated. It should finally be noted that the present work is formulated in a prospective modern coordinate-free form. Moreover, the outcome of this work is twofold. Firstly, the local expressions of the obtained results, when calculated, coincide with the existing local results. Secondly, new coordinates-free proofs have been established.

Keywords

Journal of Finsler Geometry and its Applications
Volume 1, Issue 1
July 2020
Pages 15-25

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